Estimating Quotients worksheet with 30 division problems for math practice.

Let's solve the Estimating Quotients worksheet using compatible numbers. Compatible numbers are numbers that are close to the original numbers and easy to divide mentally.

We’ll go through each problem, round the dividend and divisor to compatible numbers (usually multiples of 10 or numbers that divide evenly), then estimate the quotient.

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Guidelines for Estimating:

- Round the dividend and divisor so they are easier to divide.
- Keep the numbers close to the original values.
- Use mental math to divide.

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Now let’s solve each one:

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1. 324 ÷ 5
→ 325 ÷ 5 = 65
✔ Estimate: 65

2. 567 ÷ 15
→ 570 ÷ 15 = 38 (since 15 × 38 = 570)
✔ Estimate: 38

3. 268 ÷ 20
→ 270 ÷ 20 = 13.5 → ≈ 14
✔ Estimate: 14

4. 345 ÷ 50
→ 350 ÷ 50 = 7
✔ Estimate: 7

5. 326 ÷ 24
→ 300 ÷ 25 = 12 (close to actual)
Or 320 ÷ 20 = 16 → better to use 320 ÷ 24 ≈ 13.3 → round to 13
✔ Estimate: 13

6. 523 ÷ 3
→ 510 ÷ 3 = 170 (but 523 is closer to 540)
→ 540 ÷ 3 = 180
✔ Estimate: 180

7. 251 ÷ 20
→ 250 ÷ 20 = 12.5 → ≈ 13
✔ Estimate: 13

8. 123 ÷ 15
→ 120 ÷ 15 = 8
✔ Estimate: 8

9. 321 ÷ 12
→ 300 ÷ 12 = 25; 324 ÷ 12 = 27 → 321 is close to 324
→ 324 ÷ 12 = 27 → estimate 27
✔ Estimate: 27

10. 562 ÷ 22
→ 550 ÷ 22 = 25 (since 22×25=550)
✔ Estimate: 25

11. 675 ÷ 7
→ 672 ÷ 7 = 96 (7×96=672), close to 675
→ So, 675 ÷ 7 ≈ 96
✔ Estimate: 96

12. 321 ÷ 9
→ 324 ÷ 9 = 36 → 321 is close
→ 321 ÷ 9 ≈ 36
✔ Estimate: 36

13. 765 ÷ 17
→ 765 ÷ 17 → 17×45 = 765 → exact!
✔ Estimate: 45

14. 862 ÷ 19
→ 855 ÷ 19 = 45 (19×45=855), 862 is close
→ ≈ 45
✔ Estimate: 45

15. 543 ÷ 5
→ 540 ÷ 5 = 108
✔ Estimate: 108

16. 652 ÷ 12
→ 660 ÷ 12 = 55 → but 652 is less
→ 648 ÷ 12 = 54 → 652 ≈ 648
✔ Estimate: 54

17. 761 ÷ 11
→ 770 ÷ 11 = 70 → too high
→ 750 ÷ 11 ≈ 68.2 → try 770 - 11 = 759 → 759 ÷ 11 = 69
→ 761 ≈ 759 → 69
✔ Estimate: 69

18. 453 ÷ 12
→ 450 ÷ 12 = 37.5 → ≈ 38
✔ Estimate: 38

19. 321 ÷ 8
→ 320 ÷ 8 = 40
✔ Estimate: 40

20. 672 ÷ 11
→ 660 ÷ 11 = 60 → 672 - 660 = 12 → 12/11 ≈ 1.1 → total ≈ 61.1
→ But use 672 ÷ 11 ≈ 61
✔ Estimate: 61

21. 321 ÷ 19
→ 380 ÷ 19 = 20 → too high
→ 320 ÷ 20 = 16 → but 19×16 = 304 → 19×17 = 323 → close
→ 321 ÷ 19 ≈ 17
✔ Estimate: 17

22. 524 ÷ 12
→ 540 ÷ 12 = 45 → too high
→ 528 ÷ 12 = 44 → 524 ≈ 528 → 44
✔ Estimate: 44

23. 756 ÷ 23
→ 759 ÷ 23 = 33 (23×33 = 759) → 756 is very close
→ ≈ 33
✔ Estimate: 33

24. 782 ÷ 8
→ 784 ÷ 8 = 98 → 782 ≈ 784 → 98
✔ Estimate: 98

25. 541 ÷ 11
→ 550 ÷ 11 = 50 → 541 is less
→ 541 ÷ 11 ≈ 49.2 → ≈ 49
✔ Estimate: 49

26. 512 ÷ 7
→ 511 ÷ 7 = 73 → 7×73 = 511 → 512 ≈ 73
✔ Estimate: 73

27. 876 ÷ 9
→ 873 ÷ 9 = 97 → 9×97 = 873 → 876 ≈ 873 → 97
✔ Estimate: 97

28. 519 ÷ 40
→ 520 ÷ 40 = 13
✔ Estimate: 13

29. 987 ÷ 33
→ 990 ÷ 33 = 30 → 987 ≈ 990 → 30
✔ Estimate: 30

30. 298 ÷ 12
→ 300 ÷ 12 = 25 → 298 ≈ 300 → 25
✔ Estimate: 25

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✔ Final Answers (Estimated Quotients):

| Problem | Estimate |
|--------|---------|
| 1. 324 ÷ 5 | 65 |
| 2. 567 ÷ 15 | 38 |
| 3. 268 ÷ 20 | 14 |
| 4. 345 ÷ 50 | 7 |
| 5. 326 ÷ 24 | 13 |
| 6. 523 ÷ 3 | 180 |
| 7. 251 ÷ 20 | 13 |
| 8. 123 ÷ 15 | 8 |
| 9. 321 ÷ 12 | 27 |
|10. 562 ÷ 22 | 25 |
|11. 675 ÷ 7 | 96 |
|12. 321 ÷ 9 | 36 |
|13. 765 ÷ 17 | 45 |
|14. 862 ÷ 19 | 45 |
|15. 543 ÷ 5 | 108 |
|16. 652 ÷ 12 | 54 |
|17. 761 ÷ 11 | 69 |
|18. 453 ÷ 12 | 38 |
|19. 321 ÷ 8 | 40 |
|20. 672 ÷ 11 | 61 |
|21. 321 ÷ 19 | 17 |
|22. 524 ÷ 12 | 44 |
|23. 756 ÷ 23 | 33 |
|24. 782 ÷ 8 | 98 |
|25. 541 ÷ 11 | 49 |
|26. 512 ÷ 7 | 73 |
|27. 876 ÷ 9 | 97 |
|28. 519 ÷ 40 | 13 |
|29. 987 ÷ 33 | 30 |
|30. 298 ÷ 12 | 25 |

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🔍 Summary:

To estimate quotients using compatible numbers, we:
- Round the numbers to nearby values that are easier to divide.
- Use multiplication facts or known division results.
- Aim for a quick, reasonable approximation.

This method helps in checking division answers and building number sense.

Let me know if you'd like this as a printable answer key!